Article
Engineering, Multidisciplinary
Xiangming Zhang, Zhihua Liu
Summary: In this study, a predator-prey model with predator-age structure and predator-prey reaction time delay was investigated. By employing theoretical analysis and numerical simulations, the research identified the emergence of periodic oscillations under certain parameter values and examined the influence of different parameter values on the dynamic behavior of the system.
APPLIED MATHEMATICAL MODELLING
(2021)
Article
Mathematics
Jiao Jiang, Xiushuai Li, Xiaotian Wu
Summary: In this paper, a bioeconomic predator-prey model with Michaelis-Menten type prey harvesting and general functional response is proposed and described by a differential-algebraic system. An equivalent parametric system is derived using local parameterization, and its dynamics in terms of local stability and Hopf bifurcation are investigated. The economic profit is chosen as the bifurcation parameter to prove the occurrence of Hopf bifurcation near the interior equilibrium. Moreover, the first Lyapunov coefficient is calculated to study the direction of Hopf bifurcation and the stability of bifurcated periodic solutions based on the normal form theory. Numerical simulations are conducted to demonstrate the analytical results.
BULLETIN OF THE MALAYSIAN MATHEMATICAL SCIENCES SOCIETY
(2023)
Article
Mathematics, Interdisciplinary Applications
Binfeng Xie, Zhengce Zhang, Na Zhang
Summary: This study investigates a prey-predator system with Holling type II response function, Michaelis-Menten type capture, and fear effect. The existence and stability of equilibria, occurrence of Hopf bifurcation, and influence of fear effect and harvesting coefficient on the system are discussed. Numerical simulations are conducted to illustrate the results.
INTERNATIONAL JOURNAL OF BIFURCATION AND CHAOS
(2021)
Article
Mathematics, Applied
Ming Liu, Dongpo Hu, Fanwei Meng
Summary: Predation relationship plays a crucial role in ecosystems and researching this relationship is essential for understanding the dynamics of ecosystems.
DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS-SERIES S
(2021)
Article
Mathematics, Interdisciplinary Applications
Fatao Wang, Ruizhi Yang
Summary: In this paper, we investigate a cross-diffusion predator-prey system with Holling type functional response. We analyze the local stability, Turing instability, spatial pattern formation, Hopf and Turing-Hopf bifurcation of the equilibrium. Numerical simulation reveals that the system experiences cross-diffusion-driven instability and exhibits various patterns such as spots, stripe-spot mixtures, and labyrinthine patterns. The study also shows that the intrinsic growth rate coefficient and the environmental carrying capacity coefficient are crucial factors for the stability of the predator-prey system.
CHAOS SOLITONS & FRACTALS
(2023)
Article
Mathematics
Ruizhi Yang, Xiao Zhao, Yong An
Summary: In this study, a delayed predator-prey model with diffusion and anti-predator behavior is investigated. The stability of the positive equilibrium is analyzed, and the existence of Hopf bifurcation is discussed based on the Hopf bifurcation theory. The properties of Hopf bifurcation are derived using the theory of center manifold and normal form method. Finally, the impact of time delay on the model is examined through numerical simulations.
Article
Mathematics
Ruizhi Yang, Qiannan Song, Yong An
Summary: This paper considers a diffusive predator-prey system with a functional response that increases in both predator and prey densities. The Turing instability and Hopf bifurcation are studied by analyzing the characteristic roots of the system. By calculating the normal form of the Turing-Hopf bifurcation and conducting numerical simulations, the dynamic properties of different types of solutions in each parameter region of the phase diagram are found to be extremely rich.
Article
Mathematics, Applied
Yan Li, Zhiyi Lv, Xiuzhen Fan
Summary: This paper focuses on a diffusive predator-prey model with prey-taxis and prey-stage structure under the homogeneous Neumann boundary condition. The stability of the unique positive constant equilibrium of the predator-prey model is determined. Hopf bifurcation and steady-state bifurcation are also investigated.
MATHEMATICAL METHODS IN THE APPLIED SCIENCES
(2023)
Article
Engineering, Mechanical
Ruizhi Yang, Chenxuan Nie, Dan Jin
Summary: This paper investigates a delayed diffusive predator-prey model with nonlocal competition and habitat complexity. The local stability of coexisting equilibrium is studied by analyzing the eigenvalue spectrum. Time delay inducing Hopf bifurcation is explored using time delay as a bifurcation parameter. Conditions for determining the bifurcation direction and stability of the bifurcating periodic solution are derived using the normal form method and center manifold theorem. The results suggest that only the combination of nonlocal competition and diffusion can induce stably spatial inhomogeneous bifurcating periodic solutions.
NONLINEAR DYNAMICS
(2022)
Article
Mathematics, Applied
Binhao Hong, Chunrui Zhang
Summary: In this paper, the dynamical behavior of a predator-prey model with discrete time is explored through theoretical analysis and numerical simulation. The existence and stability of four equilibria are analyzed, with Flip bifurcation and Hopf bifurcation occurring at the unique positive equilibrium point. Chaotic cases are observed at some corresponding internal equilibria when small perturbations are applied to the bifurcation parameter. Numerical simulations using maximum Lyapunov exponent and phase diagrams reveal a complex dynamical behavior.
Article
Mathematics
Yining Xie, Jing Zhao, Ruizhi Yang
Summary: This paper proposes a diffusive predator-prey model with a strong Allee effect and nonlocal competition in the prey and a fear effect and gestation delay in the predator. The study mainly focuses on the local stability of the coexisting equilibrium and the existence and properties of Hopf bifurcation. Bifurcation diagrams with the fear effect parameter (s) and the Allee effect parameter (a) are provided, showing that the stable region of the coexisting equilibrium increases (or decreases) with an increase in the fear effect parameter (s) (or the Allee effect parameter (a)). The results demonstrate that the fear effect parameter (s), the Allee effect parameter (a), and gestation delay (t) can be utilized to control the growth of prey and predator populations.
Article
Mathematics, Applied
Chenxuan Nie, Dan Jin, Ruizhi Yang
Summary: This study considers a delayed diffusive predator-prey system with nonlocal competition and generalist predators. The local stability of the positive equilibrium and Hopf bifurcation at positive equilibrium is investigated using time delay as a parameter. Additionally, the properties of Hopf bifurcation are analyzed using the center manifold theorem and normal form method. It is found that time delays can influence the stability of the positive equilibrium and induce spatially inhomogeneous periodic oscillation of prey and predator population densities.
Article
Mathematics
Jialin Chen, Zhenliang Zhu, Xiaqing He, Fengde Chen
Summary: This paper studies a discrete Leslie-Gower predator-prey system with Michaelis-Menten type harvesting, obtains conditions on the existence and stability of fixed points, and shows through numerical simulations that the discrete system exhibits much richer dynamical behaviors compared to the continuous analog.
Article
Mathematics, Applied
Soufiane Bentout, Salih Djilali, Abdon Atangana
Summary: In this study, an age-structured prey-predator model with infection was proposed to examine the effect of predator maturation age on the interaction between predator and prey, as well as the spread of infectious disease. It was found that the minimal maturation duration can impact the behavior of the solution, potentially leading to periodic solutions generated by Hopf bifurcation for three different equilibrium states. The mathematical results were numerically validated using graphical illustrations.
MATHEMATICAL METHODS IN THE APPLIED SCIENCES
(2022)
Article
Mathematics, Applied
Yudan Ma, Ming Zhao, Yunfei Du
Summary: In this study, a predator-prey model with strong Allee effect and Holling type II functional response is proposed and investigated. Through dynamical analysis, the existence of equilibria and bifurcations of the system are derived. It is found that the strong Allee effect plays a crucial role in the dynamics of the system.
Article
Mathematics, Applied
Melanie Kobras, Valerio Lucarini, Maarten H. P. Ambaum
Summary: In this study, a minimal dynamical system derived from the classical Phillips two-level model is introduced to investigate the interaction between eddies and mean flow. The study finds that the horizontal shape of the eddies can lead to three distinct dynamical regimes, and these regimes undergo transitions depending on the intensity of external baroclinic forcing. Additionally, the study provides insights into the continuous or discontinuous transitions of atmospheric properties between different regimes.
PHYSICA D-NONLINEAR PHENOMENA
(2024)
Article
Mathematics, Applied
Shu-hong Xue, Yun-yun Yang, Biao Feng, Hai-long Yu, Li Wang
Summary: This research focuses on the robustness of multiplex networks and proposes a new index to measure their stability under malicious attacks. The effectiveness of this method is verified in real multiplex networks.
PHYSICA D-NONLINEAR PHENOMENA
(2024)
Article
Mathematics, Applied
Julien Nespoulous, Guillaume Perrin, Christine Funfschilling, Christian Soize
Summary: This paper focuses on optimizing driver commands to limit energy consumption of trains under punctuality and security constraints. A four-step approach is proposed, involving simplified modeling, parameter identification, reformulation of the optimization problem, and using evolutionary algorithms. The challenge lies in integrating uncertainties into the optimization problem.
PHYSICA D-NONLINEAR PHENOMENA
(2024)
Article
Mathematics, Applied
Alain Bourdier, Jean-Claude Diels, Hassen Ghalila, Olivier Delage
Summary: In this article, the influence of a turbulent atmosphere on the growth of modulational instability, which is the cause of multiple filamentation, is studied. It is found that considering the stochastic behavior of the refractive index leads to a decrease in the growth rate of this instability. Good qualitative agreement between analytical and numerical results is obtained.
PHYSICA D-NONLINEAR PHENOMENA
(2024)
Article
Mathematics, Applied
Ling An, Liming Ling, Xiaoen Zhang
Summary: In this paper, an integrable fractional derivative nonlinear Schrodinger equation is proposed and a reconstruction formula of the solution is obtained by constructing an appropriate Riemann-Hilbert problem. The explicit fractional N-soliton solution and the rigorous verification of the fractional one-soliton solution are presented.
PHYSICA D-NONLINEAR PHENOMENA
(2024)
Article
Mathematics, Applied
Marzia Bisi, Nadia Loy
Summary: This paper proposes and investigates general kinetic models with transition probabilities that can describe the simultaneous change of multiple microscopic states of the interacting agents. The mathematical properties of the kinetic model are proved, and the quasi-invariant asymptotic regime is studied and compared with other models. Numerical tests are performed to demonstrate the time evolution of distribution functions and macroscopic fields.
PHYSICA D-NONLINEAR PHENOMENA
(2024)
Article
Mathematics, Applied
Carlos A. Pires, David Docquier, Stephane Vannitsem
Summary: This study presents a general theory for computing information transfers in nonlinear stochastic systems driven by deterministic forcings and additive and/or multiplicative noises. It extends the Liang-Kleeman framework of causality inference to nonlinear cases based on information transfer across system variables. The study introduces an effective method called the 'Causal Sensitivity Method' (CSM) for computing the rates of Shannon entropy transfer between selected causal and consequential variables. The CSM method is robust, cheaper, and less data-demanding than traditional methods, and it opens new perspectives on real-world applications.
PHYSICA D-NONLINEAR PHENOMENA
(2024)
Article
Mathematics, Applied
Feiting Fan, Minzhi Wei
Summary: This paper focuses on the existence of periodic and solitary waves for a quintic Benjamin-Bona-Mahony (BBM) equation with distributed delay and diffused perturbation. By transforming the corresponding traveling wave equation into a three-dimensional dynamical system and applying geometric singular perturbation theory, the existence of periodic and solitary waves are established. The uniqueness of periodic waves and the monotonicity of wave speed are also analyzed.
PHYSICA D-NONLINEAR PHENOMENA
(2024)
Article
Mathematics, Applied
Wangbo Luo, Yanxiang Zhao
Summary: We propose a generalized Ohta-Kawasaki model to study the nonlocal effect on pattern formation in binary systems with long-range interactions. In the 1D case, the model displays similar bubble patterns as the standard model, but Fourier analysis reveals that the optimal number of bubbles for the generalized model may have an upper bound.
PHYSICA D-NONLINEAR PHENOMENA
(2024)
Article
Mathematics, Applied
Corentin Correia, Ana Cristina Moreira Freitas, Jorge Milhazes Freitas
Summary: The emergence of clustering of rare events is due to periodicity, where fast returns to target sets lead to a bulk of high observations. In this research, we explore the potential of a new mechanism to create clustering of rare events by linking observable functions to a finite number of points belonging to the same orbit. We show that with the right choice of system and observable, any given cluster size distribution can be obtained.
PHYSICA D-NONLINEAR PHENOMENA
(2024)
Article
Mathematics, Applied
Enyu Fan, Changpin Li
Summary: This paper numerically studies the Allen-Cahn equations with different kinds of time fractional derivatives and investigates the influences of time derivatives on the solutions of the considered models.
PHYSICA D-NONLINEAR PHENOMENA
(2024)
Article
Mathematics, Applied
Yuhang Zhu, Yinghao Zhao, Chaolin Song, Zeyu Wang
Summary: In this study, a novel approach called Time-Variant Reliability Updating (TVRU) is proposed, which integrates Kriging-based time-dependent reliability with parallel learning. This method enhances risk assessment in complex systems, showcasing exceptional efficiency and accuracy.
PHYSICA D-NONLINEAR PHENOMENA
(2024)
Article
Mathematics, Applied
Chiara Cecilia Maiocchi, Valerio Lucarini, Andrey Gritsun, Yuzuru Sato
Summary: The predictability of weather and climate is influenced by the state-dependent nature of atmospheric systems. The presence of special atmospheric states, such as blockings, is associated with anomalous instability. Chaotic systems, like the attractor of the Lorenz '96 model, exhibit heterogeneity in their dynamical properties, including the number of unstable dimensions. The variability of unstable dimensions is linked to the presence of finite-time Lyapunov exponents that fluctuate around zero. These findings have implications for understanding the structural stability and behavior modeling of high-dimensional chaotic systems.
PHYSICA D-NONLINEAR PHENOMENA
(2024)
Article
Mathematics, Applied
Christian Klein, Goksu Oruc
Summary: A numerical study on the fractional Camassa-Holm equations is conducted to construct smooth solitary waves and investigate their stability. The long-time behavior of solutions for general localized initial data from the Schwartz class of rapidly decreasing functions is also studied. Additionally, the appearance of dispersive shock waves is explored.
PHYSICA D-NONLINEAR PHENOMENA
(2024)
Article
Mathematics, Applied
Vasily E. Tarasov
Summary: This paper extends the standard action principle and the first Noether theorem to consider the general form of nonlocality in time and describes dissipative and non-Lagrangian nonlinear systems. The general fractional calculus is used to handle a wide class of nonlocalities in time compared to the usual fractional calculus. The nonlocality is described by a pair of operator kernels belonging to the Luchko set. The non-holonomic variation equations of the Sedov type are used to describe the motion equations of a wide class of dissipative and non-Lagrangian systems. Additionally, the equations of motion are considered not only with general fractional derivatives but also with general fractional integrals. An application example is presented.
PHYSICA D-NONLINEAR PHENOMENA
(2024)